{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SARIMAX: Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook replicates examples from the Stata ARIMA time series estimation and postestimation documentation.\n",
    "\n",
    "First, we replicate the four estimation examples http://www.stata.com/manuals13/tsarima.pdf:\n",
    "\n",
    "1. ARIMA(1,1,1) model on the U.S. Wholesale Price Index (WPI) dataset.\n",
    "2. Variation of example 1 which adds an MA(4) term to the ARIMA(1,1,1) specification to allow for an additive seasonal effect.\n",
    "3. ARIMA(2,1,0) x (1,1,0,12) model of monthly airline data. This example allows a multiplicative seasonal effect.\n",
    "4. ARMA(1,1) model with exogenous regressors; describes consumption as an autoregressive process on which also the money supply is assumed to be an explanatory variable.\n",
    "\n",
    "Second, we demonstrate postestimation capabilities to replicate http://www.stata.com/manuals13/tsarimapostestimation.pdf. The model from example 4 is used to demonstrate:\n",
    "\n",
    "1. One-step-ahead in-sample prediction\n",
    "2. n-step-ahead out-of-sample forecasting\n",
    "3. n-step-ahead in-sample dynamic prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy.stats import norm\n",
    "import statsmodels.api as sm\n",
    "import matplotlib.pyplot as plt\n",
    "from datetime import datetime\n",
    "import requests\n",
    "from io import BytesIO\n",
    "# Register converters to avoid warnings\n",
    "pd.plotting.register_matplotlib_converters()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ARIMA Example 1: Arima\n",
    "\n",
    "As can be seen in the graphs from Example 2, the Wholesale price index (WPI) is growing over time (i.e. is not stationary). Therefore an ARMA model is not a good specification. In this first example, we consider a model where the original time series is assumed to be integrated of order 1, so that the difference is assumed to be stationary, and fit a model with one autoregressive lag and one moving average lag, as well as an intercept term.\n",
    "\n",
    "The postulated data process is then:\n",
    "\n",
    "$$\n",
    "\\Delta y_t = c + \\phi_1 \\Delta y_{t-1} + \\theta_1 \\epsilon_{t-1} + \\epsilon_{t}\n",
    "$$\n",
    "\n",
    "where $c$ is the intercept of the ARMA model, $\\Delta$ is the first-difference operator, and we assume $\\epsilon_{t} \\sim N(0, \\sigma^2)$. This can be rewritten to emphasize lag polynomials as (this will be useful in example 2, below):\n",
    "\n",
    "$$\n",
    "(1 - \\phi_1 L ) \\Delta y_t = c + (1 + \\theta_1 L) \\epsilon_{t}\n",
    "$$\n",
    "\n",
    "where $L$ is the lag operator.\n",
    "\n",
    "Notice that one difference between the Stata output and the output below is that Stata estimates the following model:\n",
    "\n",
    "$$\n",
    "(\\Delta y_t - \\beta_0) = \\phi_1 ( \\Delta y_{t-1} - \\beta_0) + \\theta_1 \\epsilon_{t-1} + \\epsilon_{t}\n",
    "$$\n",
    "\n",
    "where $\\beta_0$ is the mean of the process $y_t$. This model is equivalent to the one estimated in the statsmodels SARIMAX class, but the interpretation is different. To see the equivalence, note that:\n",
    "\n",
    "$$\n",
    "(\\Delta y_t - \\beta_0) = \\phi_1 ( \\Delta y_{t-1} - \\beta_0) + \\theta_1 \\epsilon_{t-1} + \\epsilon_{t} \\\\\n",
    "\\Delta y_t = (1 - \\phi_1) \\beta_0 + \\phi_1 \\Delta y_{t-1} + \\theta_1 \\epsilon_{t-1} + \\epsilon_{t}\n",
    "$$\n",
    "\n",
    "so that $c = (1 - \\phi_1) \\beta_0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                           Statespace Model Results                           \n",
      "==============================================================================\n",
      "Dep. Variable:                    wpi   No. Observations:                  124\n",
      "Model:               SARIMAX(1, 1, 1)   Log Likelihood                -135.351\n",
      "Date:                Tue, 24 Dec 2019   AIC                            278.703\n",
      "Time:                        15:04:48   BIC                            289.951\n",
      "Sample:                    01-01-1960   HQIC                           283.272\n",
      "                         - 10-01-1990                                         \n",
      "Covariance Type:                  opg                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "intercept      0.0943      0.068      1.389      0.165      -0.039       0.227\n",
      "ar.L1          0.8742      0.055     16.028      0.000       0.767       0.981\n",
      "ma.L1         -0.4120      0.100     -4.119      0.000      -0.608      -0.216\n",
      "sigma2         0.5257      0.053      9.849      0.000       0.421       0.630\n",
      "===================================================================================\n",
      "Ljung-Box (Q):                       37.12   Jarque-Bera (JB):                 9.78\n",
      "Prob(Q):                              0.60   Prob(JB):                         0.01\n",
      "Heteroskedasticity (H):              15.93   Skew:                             0.28\n",
      "Prob(H) (two-sided):                  0.00   Kurtosis:                         4.26\n",
      "===================================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n"
     ]
    }
   ],
   "source": [
    "# Dataset\n",
    "wpi1 = requests.get('https://www.stata-press.com/data/r12/wpi1.dta').content\n",
    "data = pd.read_stata(BytesIO(wpi1))\n",
    "data.index = data.t\n",
    "# Set the frequency\n",
    "data.index.freq=\"QS-OCT\"\n",
    "\n",
    "# Fit the model\n",
    "mod = sm.tsa.statespace.SARIMAX(data['wpi'], trend='c', order=(1,1,1))\n",
    "res = mod.fit(disp=False)\n",
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus the maximum likelihood estimates imply that for the process above, we have:\n",
    "\n",
    "$$\n",
    "\\Delta y_t = 0.1050 + 0.8742 \\Delta y_{t-1} - 0.4120 \\epsilon_{t-1} + \\epsilon_{t}\n",
    "$$\n",
    "\n",
    "where $\\epsilon_{t} \\sim N(0, 0.5257)$. Finally, recall that $c = (1 - \\phi_1) \\beta_0$, and here $c = 0.0943$ and $\\phi_1 = 0.8742$. To compare with the output from Stata, we could calculate the mean:\n",
    "\n",
    "$$\\beta_0 = \\frac{c}{1 - \\phi_1} = \\frac{0.0943}{1 - 0.8742} = 0.7496$$\n",
    "\n",
    "**Note**: these values are slightly different from the values in the Stata documentation because the optimizer in statsmodels has found parameters here that yield a higher likelihood. Nonetheless, they are very close."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ARIMA Example 2: Arima with additive seasonal effects\n",
    "\n",
    "This model is an extension of that from example 1. Here the data is assumed to follow the process:\n",
    "\n",
    "$$\n",
    "\\Delta y_t = c + \\phi_1 \\Delta y_{t-1} + \\theta_1 \\epsilon_{t-1} + \\theta_4 \\epsilon_{t-4} + \\epsilon_{t}\n",
    "$$\n",
    "\n",
    "The new part of this model is that there is allowed to be a annual seasonal effect (it is annual even though the periodicity is 4 because the dataset is quarterly). The second difference is that this model uses the log of the data rather than the level.\n",
    "\n",
    "Before estimating the dataset, graphs showing:\n",
    "\n",
    "1. The time series (in logs)\n",
    "2. The first difference of the time series (in logs)\n",
    "3. The autocorrelation function\n",
    "4. The partial autocorrelation function.\n",
    "\n",
    "From the first two graphs, we note that the original time series does not appear to be stationary, whereas the first-difference does. This supports either estimating an ARMA model on the first-difference of the data, or estimating an ARIMA model with 1 order of integration (recall that we are taking the latter approach). The last two graphs support the use of an ARMA(1,1,1) model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Dataset\n",
    "data = pd.read_stata(BytesIO(wpi1))\n",
    "data.index = data.t\n",
    "data.index.freq=\"QS-OCT\"\n",
    "\n",
    "data['ln_wpi'] = np.log(data['wpi'])\n",
    "data['D.ln_wpi'] = data['ln_wpi'].diff()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1080x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Graph data\n",
    "fig, axes = plt.subplots(1, 2, figsize=(15,4))\n",
    "\n",
    "# Levels\n",
    "axes[0].plot(data.index._mpl_repr(), data['wpi'], '-')\n",
    "axes[0].set(title='US Wholesale Price Index')\n",
    "\n",
    "# Log difference\n",
    "axes[1].plot(data.index._mpl_repr(), data['D.ln_wpi'], '-')\n",
    "axes[1].hlines(0, data.index[0], data.index[-1], 'r')\n",
    "axes[1].set(title='US Wholesale Price Index - difference of logs');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Graph data\n",
    "fig, axes = plt.subplots(1, 2, figsize=(15,4))\n",
    "\n",
    "fig = sm.graphics.tsa.plot_acf(data.iloc[1:]['D.ln_wpi'], lags=40, ax=axes[0])\n",
    "fig = sm.graphics.tsa.plot_pacf(data.iloc[1:]['D.ln_wpi'], lags=40, ax=axes[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To understand how to specify this model in statsmodels, first recall that from example 1 we used the following code to specify the ARIMA(1,1,1) model:\n",
    "\n",
    "```python\n",
    "mod = sm.tsa.statespace.SARIMAX(data['wpi'], trend='c', order=(1,1,1))\n",
    "```\n",
    "\n",
    "The `order` argument is a tuple of the form `(AR specification, Integration order, MA specification)`. The integration order must be an integer (for example, here we assumed one order of integration, so it was specified as 1. In a pure ARMA model where the underlying data is already stationary, it would be 0).\n",
    "\n",
    "For the AR specification and MA specification components, there are two possibilities. The first is to specify the **maximum degree** of the corresponding lag polynomial, in which case the component is an integer. For example, if we wanted to specify an ARIMA(1,1,4) process, we would use:\n",
    "\n",
    "```python\n",
    "mod = sm.tsa.statespace.SARIMAX(data['wpi'], trend='c', order=(1,1,4))\n",
    "```\n",
    "\n",
    "and the corresponding data process would be:\n",
    "\n",
    "$$\n",
    "y_t = c + \\phi_1 y_{t-1} + \\theta_1 \\epsilon_{t-1} + \\theta_2 \\epsilon_{t-2} + \\theta_3 \\epsilon_{t-3} + \\theta_4 \\epsilon_{t-4} + \\epsilon_{t}\n",
    "$$\n",
    "\n",
    "or\n",
    "\n",
    "$$\n",
    "(1 - \\phi_1 L)\\Delta y_t = c + (1 + \\theta_1 L + \\theta_2 L^2 + \\theta_3 L^3 + \\theta_4 L^4) \\epsilon_{t}\n",
    "$$\n",
    "\n",
    "When the specification parameter is given as a maximum degree of the lag polynomial, it implies that all polynomial terms up to that degree are included. Notice that this is *not* the model we want to use, because it would include terms for $\\epsilon_{t-2}$ and $\\epsilon_{t-3}$, which we do not want here.\n",
    "\n",
    "What we want is a polynomial that has terms for the 1st and 4th degrees, but leaves out the 2nd and 3rd terms. To do that, we need to provide a tuple for the specification parameter, where the tuple describes **the lag polynomial itself**. In particular, here we would want to use:\n",
    "\n",
    "```python\n",
    "ar = 1          # this is the maximum degree specification\n",
    "ma = (1,0,0,1)  # this is the lag polynomial specification\n",
    "mod = sm.tsa.statespace.SARIMAX(data['wpi'], trend='c', order=(ar,1,ma)))\n",
    "```\n",
    "\n",
    "This gives the following form for the process of the data:\n",
    "\n",
    "$$\n",
    "\\Delta y_t = c + \\phi_1 \\Delta y_{t-1} + \\theta_1 \\epsilon_{t-1} + \\theta_4 \\epsilon_{t-4} + \\epsilon_{t} \\\\\n",
    "(1 - \\phi_1 L)\\Delta y_t = c + (1 + \\theta_1 L + \\theta_4 L^4) \\epsilon_{t}\n",
    "$$\n",
    "\n",
    "which is what we want."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                             Statespace Model Results                            \n",
      "=================================================================================\n",
      "Dep. Variable:                    ln_wpi   No. Observations:                  124\n",
      "Model:             SARIMAX(1, 1, (1, 4))   Log Likelihood                 386.033\n",
      "Date:                   Tue, 24 Dec 2019   AIC                           -762.067\n",
      "Time:                           15:04:52   BIC                           -748.006\n",
      "Sample:                       01-01-1960   HQIC                          -756.355\n",
      "                            - 10-01-1990                                         \n",
      "Covariance Type:                     opg                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "intercept      0.0024      0.002      1.486      0.137      -0.001       0.006\n",
      "ar.L1          0.7803      0.095      8.255      0.000       0.595       0.966\n",
      "ma.L1         -0.3992      0.126     -3.173      0.002      -0.646      -0.153\n",
      "ma.L4          0.3092      0.120      2.577      0.010       0.074       0.544\n",
      "sigma2         0.0001   9.79e-06     11.114      0.000    8.97e-05       0.000\n",
      "===================================================================================\n",
      "Ljung-Box (Q):                       30.03   Jarque-Bera (JB):                45.09\n",
      "Prob(Q):                              0.87   Prob(JB):                         0.00\n",
      "Heteroskedasticity (H):               2.58   Skew:                             0.29\n",
      "Prob(H) (two-sided):                  0.00   Kurtosis:                         5.91\n",
      "===================================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n"
     ]
    }
   ],
   "source": [
    "# Fit the model\n",
    "mod = sm.tsa.statespace.SARIMAX(data['ln_wpi'], trend='c', order=(1,1,(1,0,0,1)))\n",
    "res = mod.fit(disp=False)\n",
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ARIMA Example 3: Airline Model\n",
    "\n",
    "In the previous example, we included a seasonal effect in an *additive* way, meaning that we added a term allowing the process to depend on the 4th MA lag. It may be instead that we want to model a seasonal effect in a multiplicative way. We often write the model then as an ARIMA $(p,d,q) \\times (P,D,Q)_s$, where the lowercase letters indicate the specification for the non-seasonal component, and the uppercase letters indicate the specification for the seasonal component; $s$ is the periodicity of the seasons (e.g. it is often 4 for quarterly data or 12 for monthly data). The data process can be written generically as:\n",
    "\n",
    "$$\n",
    "\\phi_p (L) \\tilde \\phi_P (L^s) \\Delta^d \\Delta_s^D y_t = A(t) + \\theta_q (L) \\tilde \\theta_Q (L^s) \\epsilon_t\n",
    "$$\n",
    "\n",
    "where:\n",
    "\n",
    "- $\\phi_p (L)$ is the non-seasonal autoregressive lag polynomial\n",
    "- $\\tilde \\phi_P (L^s)$ is the seasonal autoregressive lag polynomial\n",
    "- $\\Delta^d \\Delta_s^D y_t$ is the time series, differenced $d$ times, and seasonally differenced $D$ times.\n",
    "- $A(t)$ is the trend polynomial (including the intercept)\n",
    "- $\\theta_q (L)$ is the non-seasonal moving average lag polynomial\n",
    "- $\\tilde \\theta_Q (L^s)$ is the seasonal moving average lag polynomial\n",
    "\n",
    "sometimes we rewrite this as:\n",
    "\n",
    "$$\n",
    "\\phi_p (L) \\tilde \\phi_P (L^s) y_t^* = A(t) + \\theta_q (L) \\tilde \\theta_Q (L^s) \\epsilon_t\n",
    "$$\n",
    "\n",
    "where $y_t^* = \\Delta^d \\Delta_s^D y_t$. This emphasizes that just as in the simple case, after we take differences (here both non-seasonal and seasonal) to make the data stationary, the resulting model is just an ARMA model.\n",
    "\n",
    "As an example, consider the airline model ARIMA $(2,1,0) \\times (1,1,0)_{12}$, with an intercept. The data process can be written in the form above as:\n",
    "\n",
    "$$\n",
    "(1 - \\phi_1 L - \\phi_2 L^2) (1 - \\tilde \\phi_1 L^{12}) \\Delta \\Delta_{12} y_t = c + \\epsilon_t\n",
    "$$\n",
    "\n",
    "Here, we have:\n",
    "\n",
    "- $\\phi_p (L) = (1 - \\phi_1 L - \\phi_2 L^2)$\n",
    "- $\\tilde \\phi_P (L^s) = (1 - \\phi_1 L^12)$\n",
    "- $d = 1, D = 1, s=12$ indicating that $y_t^*$ is derived from $y_t$ by taking first-differences and then taking 12-th differences.\n",
    "- $A(t) = c$ is the *constant* trend polynomial (i.e. just an intercept)\n",
    "- $\\theta_q (L) = \\tilde \\theta_Q (L^s) = 1$ (i.e. there is no moving average effect)\n",
    "\n",
    "It may still be confusing to see the two lag polynomials in front of the time-series variable, but notice that we can multiply the lag polynomials together to get the following model:\n",
    "\n",
    "$$\n",
    "(1 - \\phi_1 L - \\phi_2 L^2 - \\tilde \\phi_1 L^{12} + \\phi_1 \\tilde \\phi_1 L^{13} + \\phi_2 \\tilde \\phi_1 L^{14} ) y_t^* = c + \\epsilon_t\n",
    "$$\n",
    "\n",
    "which can be rewritten as:\n",
    "\n",
    "$$\n",
    "y_t^* = c + \\phi_1 y_{t-1}^* + \\phi_2 y_{t-2}^* + \\tilde \\phi_1 y_{t-12}^* - \\phi_1 \\tilde \\phi_1 y_{t-13}^* - \\phi_2 \\tilde \\phi_1 y_{t-14}^* + \\epsilon_t\n",
    "$$\n",
    "\n",
    "This is similar to the additively seasonal model from example 2, but the coefficients in front of the autoregressive lags are actually combinations of the underlying seasonal and non-seasonal parameters.\n",
    "\n",
    "Specifying the model in statsmodels is done simply by adding the `seasonal_order` argument, which accepts a tuple of the form `(Seasonal AR specification, Seasonal Integration order, Seasonal MA, Seasonal periodicity)`. The seasonal AR and MA specifications, as before, can be expressed as a maximum polynomial degree or as the lag polynomial itself. Seasonal periodicity is an integer.\n",
    "\n",
    "For the airline model ARIMA $(2,1,0) \\times (1,1,0)_{12}$ with an intercept, the command is:\n",
    "\n",
    "```python\n",
    "mod = sm.tsa.statespace.SARIMAX(data['lnair'], order=(2,1,0), seasonal_order=(1,1,0,12))\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                 Statespace Model Results                                 \n",
      "==========================================================================================\n",
      "Dep. Variable:                       D.DS12.lnair   No. Observations:                  131\n",
      "Model:             SARIMAX(2, 0, 0)x(1, 0, 0, 12)   Log Likelihood                 240.821\n",
      "Date:                            Tue, 24 Dec 2019   AIC                           -473.643\n",
      "Time:                                    15:04:55   BIC                           -462.142\n",
      "Sample:                                02-01-1950   HQIC                          -468.970\n",
      "                                     - 12-01-1960                                         \n",
      "Covariance Type:                              opg                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "ar.L1         -0.4057      0.080     -5.045      0.000      -0.563      -0.248\n",
      "ar.L2         -0.0799      0.099     -0.809      0.419      -0.274       0.114\n",
      "ar.S.L12      -0.4723      0.072     -6.592      0.000      -0.613      -0.332\n",
      "sigma2         0.0014      0.000      8.403      0.000       0.001       0.002\n",
      "===================================================================================\n",
      "Ljung-Box (Q):                       49.89   Jarque-Bera (JB):                 0.72\n",
      "Prob(Q):                              0.14   Prob(JB):                         0.70\n",
      "Heteroskedasticity (H):               0.54   Skew:                             0.14\n",
      "Prob(H) (two-sided):                  0.04   Kurtosis:                         3.23\n",
      "===================================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n"
     ]
    }
   ],
   "source": [
    "# Dataset\n",
    "air2 = requests.get('https://www.stata-press.com/data/r12/air2.dta').content\n",
    "data = pd.read_stata(BytesIO(air2))\n",
    "data.index = pd.date_range(start=datetime(data.time[0], 1, 1), periods=len(data), freq='MS')\n",
    "data['lnair'] = np.log(data['air'])\n",
    "\n",
    "# Fit the model\n",
    "mod = sm.tsa.statespace.SARIMAX(data['lnair'], order=(2,1,0), seasonal_order=(1,1,0,12), simple_differencing=True)\n",
    "res = mod.fit(disp=False)\n",
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that here we used an additional argument `simple_differencing=True`. This controls how the order of integration is handled in ARIMA models. If `simple_differencing=True`, then the time series provided as `endog` is literally differenced and an ARMA model is fit to the resulting new time series. This implies that a number of initial periods are lost to the differencing process, however it may be necessary either to compare results to other packages (e.g. Stata's `arima` always uses  simple differencing) or if the seasonal periodicity is large.\n",
    "\n",
    "The default is `simple_differencing=False`, in which case the integration component is implemented as part of the state space formulation, and all of the original data can be used in estimation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ARIMA Example 4: ARMAX (Friedman)\n",
    "\n",
    "This model demonstrates the use of explanatory variables (the X part of ARMAX). When exogenous regressors are included, the SARIMAX module uses the concept of \"regression with SARIMA errors\" (see http://robjhyndman.com/hyndsight/arimax/ for details of regression with ARIMA errors versus alternative specifications), so that the model is specified as:\n",
    "\n",
    "$$\n",
    "y_t = \\beta_t x_t + u_t \\\\\n",
    "        \\phi_p (L) \\tilde \\phi_P (L^s) \\Delta^d \\Delta_s^D u_t = A(t) +\n",
    "            \\theta_q (L) \\tilde \\theta_Q (L^s) \\epsilon_t\n",
    "$$\n",
    "\n",
    "Notice that the first equation is just a linear regression, and the second equation just describes the process followed by the error component as SARIMA (as was described in example 3). One reason for this specification is that the estimated parameters have their natural interpretations.\n",
    "\n",
    "This specification nests many simpler specifications. For example, regression with AR(2) errors is:\n",
    "\n",
    "$$\n",
    "y_t = \\beta_t x_t + u_t \\\\\n",
    "(1 - \\phi_1 L - \\phi_2 L^2) u_t = A(t) + \\epsilon_t\n",
    "$$\n",
    "\n",
    "The model considered in this example is regression with ARMA(1,1) errors. The process is then written:\n",
    "\n",
    "$$\n",
    "\\text{consump}_t = \\beta_0 + \\beta_1 \\text{m2}_t + u_t \\\\\n",
    "(1 - \\phi_1 L) u_t = (1 - \\theta_1 L) \\epsilon_t\n",
    "$$\n",
    "\n",
    "Notice that $\\beta_0$ is, as described in example 1 above, *not* the same thing as an intercept specified by `trend='c'`. Whereas in the examples above we estimated the intercept of the model via the trend polynomial, here, we demonstrate how to estimate $\\beta_0$ itself by adding a constant to the exogenous dataset. In the output, the $beta_0$ is called `const`, whereas above the intercept $c$ was called `intercept` in the output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                           Statespace Model Results                           \n",
      "==============================================================================\n",
      "Dep. Variable:                consump   No. Observations:                   92\n",
      "Model:               SARIMAX(1, 0, 1)   Log Likelihood                -340.508\n",
      "Date:                Tue, 24 Dec 2019   AIC                            691.015\n",
      "Time:                        15:05:00   BIC                            703.624\n",
      "Sample:                    01-01-1959   HQIC                           696.105\n",
      "                         - 10-01-1981                                         \n",
      "Covariance Type:                  opg                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const        -36.0608     56.646     -0.637      0.524    -147.084      74.962\n",
      "m2             1.1220      0.036     30.824      0.000       1.051       1.193\n",
      "ar.L1          0.9348      0.041     22.717      0.000       0.854       1.016\n",
      "ma.L1          0.3091      0.089      3.488      0.000       0.135       0.483\n",
      "sigma2        93.2548     10.888      8.565      0.000      71.914     114.596\n",
      "===================================================================================\n",
      "Ljung-Box (Q):                       38.72   Jarque-Bera (JB):                23.49\n",
      "Prob(Q):                              0.53   Prob(JB):                         0.00\n",
      "Heteroskedasticity (H):              22.51   Skew:                             0.17\n",
      "Prob(H) (two-sided):                  0.00   Kurtosis:                         5.45\n",
      "===================================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n"
     ]
    }
   ],
   "source": [
    "# Dataset\n",
    "friedman2 = requests.get('https://www.stata-press.com/data/r12/friedman2.dta').content\n",
    "data = pd.read_stata(BytesIO(friedman2))\n",
    "data.index = data.time\n",
    "data.index.freq = \"QS-OCT\"\n",
    "\n",
    "# Variables\n",
    "endog = data.loc['1959':'1981', 'consump']\n",
    "exog = sm.add_constant(data.loc['1959':'1981', 'm2'])\n",
    "\n",
    "# Fit the model\n",
    "mod = sm.tsa.statespace.SARIMAX(endog, exog, order=(1,0,1))\n",
    "res = mod.fit(disp=False)\n",
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ARIMA Postestimation: Example 1 - Dynamic Forecasting\n",
    "\n",
    "Here we describe some of the post-estimation capabilities of statsmodels' SARIMAX.\n",
    "\n",
    "First, using the model from example, we estimate the parameters using data that *excludes the last few observations* (this is a little artificial as an example, but it allows considering performance of out-of-sample forecasting and facilitates comparison to Stata's documentation)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                           Statespace Model Results                           \n",
      "==============================================================================\n",
      "Dep. Variable:                consump   No. Observations:                   77\n",
      "Model:               SARIMAX(1, 0, 1)   Log Likelihood                -243.316\n",
      "Date:                Tue, 24 Dec 2019   AIC                            496.633\n",
      "Time:                        15:05:03   BIC                            508.352\n",
      "Sample:                    01-01-1959   HQIC                           501.320\n",
      "                         - 01-01-1978                                         \n",
      "Covariance Type:                  opg                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.6740     18.487      0.036      0.971     -35.559      36.907\n",
      "m2             1.0379      0.021     50.339      0.000       0.997       1.078\n",
      "ar.L1          0.8775      0.059     14.858      0.000       0.762       0.993\n",
      "ma.L1          0.2771      0.108      2.572      0.010       0.066       0.488\n",
      "sigma2        31.6979      4.683      6.769      0.000      22.520      40.876\n",
      "===================================================================================\n",
      "Ljung-Box (Q):                       46.77   Jarque-Bera (JB):                 6.05\n",
      "Prob(Q):                              0.21   Prob(JB):                         0.05\n",
      "Heteroskedasticity (H):               6.09   Skew:                             0.57\n",
      "Prob(H) (two-sided):                  0.00   Kurtosis:                         3.76\n",
      "===================================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n"
     ]
    }
   ],
   "source": [
    "# Dataset\n",
    "raw = pd.read_stata(BytesIO(friedman2))\n",
    "raw.index = raw.time\n",
    "raw.index.freq = \"QS-OCT\"\n",
    "data = raw.loc[:'1981']\n",
    "\n",
    "# Variables\n",
    "endog = data.loc['1959':, 'consump']\n",
    "exog = sm.add_constant(data.loc['1959':, 'm2'])\n",
    "nobs = endog.shape[0]\n",
    "\n",
    "# Fit the model\n",
    "mod = sm.tsa.statespace.SARIMAX(endog.loc[:'1978-01-01'], exog=exog.loc[:'1978-01-01'], order=(1,0,1))\n",
    "fit_res = mod.fit(disp=False)\n",
    "print(fit_res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we want to get results for the full dataset but using the estimated parameters (on a subset of the data)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "mod = sm.tsa.statespace.SARIMAX(endog, exog=exog, order=(1,0,1))\n",
    "res = mod.filter(fit_res.params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `predict` command is first applied here to get in-sample predictions. We use the `full_results=True` argument to allow us to calculate confidence intervals (the default output of `predict` is just the predicted values).\n",
    "\n",
    "With no other arguments, `predict` returns the one-step-ahead in-sample predictions for the entire sample."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# In-sample one-step-ahead predictions\n",
    "predict = res.get_prediction()\n",
    "predict_ci = predict.conf_int()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also get *dynamic predictions*. One-step-ahead prediction uses the true values of the endogenous values at each step to predict the next in-sample value. Dynamic predictions use one-step-ahead prediction up to some point in the dataset (specified by the `dynamic` argument); after that, the previous *predicted* endogenous values are used in place of the true endogenous values for each new predicted element.\n",
    "\n",
    "The `dynamic` argument is specified to be an *offset* relative to the `start` argument. If `start` is not specified, it is assumed to be `0`.\n",
    "\n",
    "Here we perform dynamic prediction starting in the first quarter of 1978."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Dynamic predictions\n",
    "predict_dy = res.get_prediction(dynamic='1978-01-01')\n",
    "predict_dy_ci = predict_dy.conf_int()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can graph the one-step-ahead and dynamic predictions (and the corresponding confidence intervals) to see their relative performance. Notice that up to the point where dynamic prediction begins (1978:Q1), the two are the same."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Graph\n",
    "fig, ax = plt.subplots(figsize=(9,4))\n",
    "npre = 4\n",
    "ax.set(title='Personal consumption', xlabel='Date', ylabel='Billions of dollars')\n",
    "\n",
    "# Plot data points\n",
    "data.loc['1977-07-01':, 'consump'].plot(ax=ax, style='o', label='Observed')\n",
    "\n",
    "# Plot predictions\n",
    "predict.predicted_mean.loc['1977-07-01':].plot(ax=ax, style='r--', label='One-step-ahead forecast')\n",
    "ci = predict_ci.loc['1977-07-01':]\n",
    "ax.fill_between(ci.index, ci.iloc[:,0], ci.iloc[:,1], color='r', alpha=0.1)\n",
    "predict_dy.predicted_mean.loc['1977-07-01':].plot(ax=ax, style='g', label='Dynamic forecast (1978)')\n",
    "ci = predict_dy_ci.loc['1977-07-01':]\n",
    "ax.fill_between(ci.index, ci.iloc[:,0], ci.iloc[:,1], color='g', alpha=0.1)\n",
    "\n",
    "legend = ax.legend(loc='lower right')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, graph the prediction *error*. It is obvious that, as one would suspect, one-step-ahead prediction is considerably better."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Prediction error\n",
    "\n",
    "# Graph\n",
    "fig, ax = plt.subplots(figsize=(9,4))\n",
    "npre = 4\n",
    "ax.set(title='Forecast error', xlabel='Date', ylabel='Forecast - Actual')\n",
    "\n",
    "# In-sample one-step-ahead predictions and 95% confidence intervals\n",
    "predict_error = predict.predicted_mean - endog\n",
    "predict_error.loc['1977-10-01':].plot(ax=ax, label='One-step-ahead forecast')\n",
    "ci = predict_ci.loc['1977-10-01':].copy()\n",
    "ci.iloc[:,0] -= endog.loc['1977-10-01':]\n",
    "ci.iloc[:,1] -= endog.loc['1977-10-01':]\n",
    "ax.fill_between(ci.index, ci.iloc[:,0], ci.iloc[:,1], alpha=0.1)\n",
    "\n",
    "# Dynamic predictions and 95% confidence intervals\n",
    "predict_dy_error = predict_dy.predicted_mean - endog\n",
    "predict_dy_error.loc['1977-10-01':].plot(ax=ax, style='r', label='Dynamic forecast (1978)')\n",
    "ci = predict_dy_ci.loc['1977-10-01':].copy()\n",
    "ci.iloc[:,0] -= endog.loc['1977-10-01':]\n",
    "ci.iloc[:,1] -= endog.loc['1977-10-01':]\n",
    "ax.fill_between(ci.index, ci.iloc[:,0], ci.iloc[:,1], color='r', alpha=0.1)\n",
    "\n",
    "legend = ax.legend(loc='lower left');\n",
    "legend.get_frame().set_facecolor('w')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
